This class of nonassociative algebras has been studied in [1]} to extend the notion of quantification by deformation of associative commutative algebras. Recall that a nonassociative algebra \((A,\mu )\)  is weakly associative if we have
\(\mathcal {A}_{\mu }(x_1,x_2,x_3)+\mathcal {A}_{\mu }(x_2,x_3,x_1)-\mathcal {A}_{\mu }(x_2,x_1,x_3)=0.\) 
